Question

Question
What is the ordered pair for the point of inflection in the standard form of the cube root function y=ax−h−−−−−√3+k
?(1 point)
Responses

(−h,k)
left parenthesis negative h comma k right parenthesis

(h,−k)
left parenthesis h comma negative k right parenthesis

(k,h)
left parenthesis k comma h right parenthesis

(h,k)
left parenthesis h comma k right parenthesis
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Answer 1

To find the point of inflection for the cube root function given in the form \( y = a \sqrt[3]{x - h} + k \), we analyze the properties of the function.

The standard cube root function \( y = \sqrt[3]{x} \) has an inflection point at the origin \( (0, 0) \). When we transform this function, we are applying a horizontal shift by \( h \) and a vertical shift by \( k \). The inflection point will move accordingly.

1. The horizontal shift by \( h \) means that the x-value of the inflection point becomes \( h \).
2. The vertical shift by \( k \) means that the y-value of the inflection point becomes \( k \).

Thus, the inflection point of the transformed function \( y = a \sqrt[3]{x - h} + k \) is at the point \( (h, k) \).

So, the correct response for the ordered pair for the point of inflection is:

**(h, k)**.